In AE, you use the pen or mask shape tools to create masks that can be animated. Once you make the mask you twirl down your layer settings, click on mask shape stopwatch and set a keyframe. Move the CTI(current time indicator) to a different time and change your mask.
In that video besides masking a lot of those reveals were done by animating opacity, scale along with masking.
Going to make an assuption Aaron that you are very new to AE, you should check out the page of Getting Started links that Todd Kopriva has put together.
Johnny Cuevas, Editor
Thinkck.com
“I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work.”
—THOMAS EDISON on inventing the light bulb.